Investigations of key issues on the reproducibility of high-T_c superconductivity emerging from compressed La₃Ni₂O₇

The quest for novel high-temperature superconductors is motivated by the expectations that these materials could have practical applications and that their study could lead to a better understanding of the fundamental mechanisms underlying high-temperature superconductivity. A possibly fruitful group of compounds for investigation are the nickelates.¹ Several candidates for superconductivity have been found among thin-film nickelates.^2–6 Recently, signatures of superconductivity with a transition temperature T_c near 80 K have been discovered in single-crystal La₃Ni₂O₇ under high pressure.⁷ This high-T_c compound has garnered considerable interest in the past few months, and a great number of initial advances have been made.^8–50 The results from high-resolution angle-resolved photoemission spectroscopy^21,51,52 suggest that ambient-pressure La₃Ni₂O₇ exhibits a strong correlation characteristic¹³ associated with the covalent hybridization between transition metal 3d and O 2p orbitals, which is similar to the formation of the Zhang–Rice singlet in cuprates.⁵³ In particular, the coexistence of spin-density-wave and charge-density-wave phases has been revealed at ambient pressure.^20,23 These observations suggest that La₃Ni₂O₇ has the potential to exhibit intriguing phenomena under specific nonthermal control parameters, such as pressure.

On the experimental side, although zero resistance has been observed in some compressed nickelate samples,^8,9 most others, even when cut from the same batch as such a sample, show no zero-resistance superconductivity. This anomalously irreproducible superconductivity suggests the possibility of an inhomogeneous distribution of a small amount of the superconducting phase within the crystal. In addition, the signature of the high-T_c superconductivity has also been observed in the La₃Ni₂O₇ polycrystalline samples,^9–11 but no accompanying Meissner effect has been reported in these papers. Recent experimental results regarding the characterization of La₃Ni₂O₇ single crystals have revealed the existence of minor intergrowth phases within the main phase characterized by bilayer blocks with alternating NiO₆ octahedra (referred to as 2222 or 327 phase). These intergrowth phases include the 214 phase characterized by single-layer blocks, the 4310 phase characterized by trilayer blocks, and a polymorphic phase featuring both single and trilayer blocks (referred to as 1313 phase).^{12,14,16,22,26} These results suggest that this material may exhibit a more complex physics associated with high-T_c superconductivity compared with the pure 327 phase, and this demands a comprehensive investigation.

In the study reported here, we conducted the first high-pressure measurements on the superconducting volume fraction of compressed La₃Ni₂O₇ using a modulated alternating-current (ac) susceptibility system. This system possesses the ability to detect superconducting volume fractions as low as 0.5% (the details can be found in the supplementary material). Moreover, we performed in situ resistance, Hall coefficient, and scanning transmission electron microscopy (STEM) investigations, in an attempt to clarify the anomalous superconductivity observed in compressed La₃Ni₂O₇.

Before conducting the high-pressure experiments, we performed structural characterization and resistance measurements on a single-crystal La₃Ni₂O₇ sample at ambient pressure (see the supplementary material). Single-crystal X-ray diffraction (XRD) revealed that our sample crystallized in an orthorhombic unit cell in Amam space, in good agreement with the results reported in Ref. 7. Careful examination of our XRD data revealed the presence of the 1313 phase in one of two single-crystal samples (see the supplementary material), which aligns with the findings reported by Chen et al.¹² The temperature dependence of the resistance for the ambient-pressure sample revealed metallic behavior upon cooling, consistent with reported results.⁷ In the high-pressure modulated ac susceptibility measurements, we loaded a piece of elemental vanadium, with identical shape but nearly half the volume of the La₃Ni₂O₇ sample, in the same high-pressure chamber as a reference to estimate the relative superconducting volume fraction of the La₃Ni₂O₇ sample. By comparing their diamagnetic signal magnitude, we obtained a rough estimate of the superconducting volume fraction of the La₃Ni₂O₇ sample. The pressure applied to the sample was determined through the pressure-dependent T_c of the vanadium.⁵⁴  Figure 1 shows the temperature dependence of the modulated ac susceptibility Δχ′ obtained at different pressures. Below 20.7 GPa, no superconducting transition is observed, and only the background signal is detected [Figs. 1(a)–1(c)], whereas in this pressure range, the superconducting transitions of the elemental vanadium can be clearly identified by a sudden increase in the signal above the background [the arrow indicates the onset temperature of the superconducting transition; see the insets in Figs. 1(a)–1(c)]. When the pressure is increased to 22 GPa, a “broad peak” emerges at 64.3 K [Fig. 1(d)]. According to the theory of modulated magnetic susceptibility,^55–57 this “peak” results from the superconducting transition of the sample, rather than a magnetic transition (see the supplementary material). To enhance the visibility, we mark the broad peak by light green shading in Fig. 1(d), with the background represented by a dashed line. This kind of broad peak can be observed up to 28.2 GPa, the highest pressure investigated in this run [Figs. 1(d)–1(f)].

Here, we employ the ratio of the superconducting diamagnetic signal per unit volume of the sample $(Δχ′s/Vs)$ to that of the vanadium $(Δχ′V/VV)$ to estimate the relative superconducting volume fraction in La₃Ni₂O₇, yielding a value of 0.68% (∼1%) [the sample volumes are V_s = 93 × 93 × 19.3 μm³ = 16.6926 × 10⁴ μm³ and V_V = 75 × 75 × 9.6 µm³ = 5.4 × 10⁴ μm³, and so $(Δχ′s/Vs)/(Δχ′V/VV)=(0.011/16.6926×104μm3)/(0.524/5.4×104μm3)≈0.0068.$ This suggests that the superconductivity observed in La₃Ni₂O₇ is not of a bulk nature, but rather a filamentary-like one.

Furthermore, we found that the superconducting transition temperature slightly decreases with increasing pressure, as shown in Figs. 1(d)–1(f), consistent with the resistance measurements reported in previous studies.^7–9 We then released the pressure, starting from 28.2 GPa, and found a slight increase in T_c [Figs. 1(g) and 1(h)], in which the maximum T_c reached 65.2 K at 21.2 GPa. As the pressure was further released to 17.2 GPa, the superconducting diamagnetic signal became invisible, consistent with the behavior when the pressure was increased to the same level [Figs. 1(b) and 1(c)]. This indicates that the pressure-induced transition is reversible. However, unexpectedly, in our five independent measurements on samples cut from the same batch, we observed the superconducting diamagnetic transition only once (see the supplementary material). In addition, we also performed an ac susceptibility measurement on a La₃Ni₂O₇ single-crystal sample using an unmodulated ac susceptibility system (the sample signal was detected by a single-phase-locked amplifier) and did not observe any evidence of a superconducting diamagnetic transition (see the supplementary material).

To further investigate the superconducting behavior of compressed La₃Ni₂O₇ single crystals, we conducted dc susceptibility measurements on this material and superconducting vanadium (Fig. 2). No evidence of a superconducting transition was found in La₃Ni₂O₇, although the volume of the La₃Ni₂O₇ single-crystal sample was nearly twice that of the vanadium. These results suggest that La₃Ni₂O₇ single crystals do no exhibit bulk superconductivity.

Next, we performed high-pressure resistance measurements on La₃Ni₂O₇ single-crystal samples. We did this for seven samples, but observed the presence of superconductivity with zero resistance in only one of them. Figure 3 shows the results from two of the samples (A and B). Sample A displays semiconducting-like behavior at a pressure below 7.9 GPa. Its resistance starts to drop at low temperature at 11.1 GPa [Fig. 3(a)]. This drop becomes more pronounced with increasing pressure. It approaches zero above 21.5 GPa [Fig. 3(b)]. For sample B, zero resistance is observed when the pressure is applied between 17.8 and 31.5 GPa [see the inset of Fig. 3(c)], which confirms the occurrence of a superconducting transition in La₃Ni₂O₇. Subsequently, we released the pressure from 31.5 GPa down to 5.5 GPa and observed a gradual loss of superconductivity [Fig. 3(d)], consistent with our findings from the modulated ac susceptibility measurements (Fig. 1). At 5.5 GPa, the sample returned to its semiconducting phase [Fig. 3(d)], indicating that the pressure-induced transition from the semiconducting state to the superconducting state is reversible.

Figure 4 shows a phase diagram obtained on the basis of our ac susceptibility and transport measurements on La₃Ni₂O₇. In this diagram, we have also included the density-wave-like phase transition temperatures (T_SDW and T_D) reported in Refs. 13 and 23 and the T_c values reported by other groups.^7–9 It can be seen that the application of pressure decreases the formation temperature of the density wave (DW)-like phase, but increases that of the spin-density wave (SDW)-like phase,^13,23 and then induces a superconducting (SC) transition at a critical pressure P_c above 10 GPa [Fig. 4(a)].

In addition, we conducted Hall measurements on the sample (see the supplementary material) and found that the Hall coefficient R_H remains positive across the investigated pressure range, with a notable drop at around P_c [Fig. 4(b)]. This positive Hall coefficient and the sudden change align with the trends observed in studies of Sr-doped LaNiO₂.³ As it is known that the sample undergoes a structural phase transition from an ambient-pressure orthorhombic Amam phase to a high-pressure orthorhombic Fmmm phase at the temperature of our Hall measurements,^7,19 the drop in R_H at the boundary between the DW-like and the normal state of the superconducting (SC) phases seems to be related to this pressure-induced structural phase transition. On the other hand, this change in charge carriers at a pressure around that corresponding to the emergence of superconductivity suggests that pressure-induced changes in oxygen vacancies or Ni valence states may also play a role in developing superconductivity in this material, which deserves further investigation.

The observation of a small superconducting volume fraction and the fact that it is difficult to obtain a zero-resistance state suggest that the superconductivity in La₃Ni₂O₇ is likely filamentary in nature.^17,58–61 This speculation accounts for several enigmas regarding the pressure-induced superconductivity in La₃Ni₂O₇ single-crystal samples. As an example, when conducting resistance measurements along different directions of the sample, we found that zero resistance was observed in only one direction, but not in the others, despite having the onset T_c values being the same in both directions.

To provide more evidence for the proposed filamentary-like superconductivity in compressed La₃Ni₂O₇, we performed high-pressure resistance measurements on a sample using various current values (ranging from 0.01 to 1 mA). We found non-Ohmic behavior below T_c, which is consistent with other results reported recently,²² and nonlinear V–I characteristics (see the supplementary material), supporting our proposal that the superconductivity in La₃Ni₂O₇ is nonbulk in nature, but instead is filamentary-like.

To further understand the perplexing superconducting behavior of La₃Ni₂O₇, we performed STEM investigations on both single-crystal and polycrystalline samples (Fig. 5). It was found that their predominant phase was the La₃Ni₂O₇ (327) phase with the 2222 stacking sequence, while the minor phases (<5%) consisted of the La₄Ni₃O₁₀ (4310) and La₂Ni₁O₄ (214) phases in the polycrystalline sample [Figs. 5(a) and 5(b)] and the 4310 phase in the single-crystal sample [Figs. 5(c)–5(t)]. Furthermore, interfaces were observed within both the superconducting polycrystalline sample [Fig. 5(a)] and the single-crystal sample [Figs. 5(c)–5(n)]. Careful examination of the superconducting single-crystal sample revealed the existence of the 327 and 4310 phases and their mixed phase at the interfaces [Figs. 5(o)–5(q)]. By performing fast Fourier transforms (FFTs) based on the corresponding electron diffraction results [Figs. 5(r)–5(t)], we obtained the averaged d-spacing value profiles of the 327 and 4310 phases and their mixed phase at the interface [Fig. 5(u)]. These results indicate that La₃Ni₂O₇ exhibits significant inhomogeneity.

Similar to what has been observed in cuprate superconductors,^62–65 the deviation from stoichiometric oxygen content in La₃Ni₂O₇ appears to have a significant impact on the presence of superconductivity.¹⁷ To establish the connection of the oxygen content with the presence of superconductivity in La₃Ni₂O_7+δ (where δ denotes the oxygen vacancy), we performed comprehensive investigations starting with the synthesis of polycrystalline samples by a sol–gel method (see the supplementary material). Characterization of the as-grown samples showed that they could be well indexed by the orthorhombic structure in the Amam space group (see the supplementary material), which is consistent with the structure of the single-crystal sample reported in Ref. 7. The oxygen content of the as-grown samples was estimated to be about 6.88 (i.e., an oxygen vacancy of δ = −0.12), as determined by thermogravimetric analysis (see the supplementary material). Subsequently, we adjusted the oxygen content over a wide range using an electrochemical method^66,67 (see the supplementary material), and measured the resistance and modulated ac susceptibility on the same sample in a diamond anvil cell. As shown in Fig. 6(a), superconductivity was observed only within a specific range of oxygen content, from 6.88 (δ = −0.12) to 7.42 (δ = 0.42). Intriguingly, within this range, the maximum T_c value remained nearly unchanged, which suggests that when the oxygen content lies in an appropriate range, it no longer significantly affects the maximum T_c value. On the basis of these results, we determined the upper and lower bounds on the oxygen content required for the development of superconductivity to be about 7.35 and 6.89, respectively. Outside this range, superconductivity was no longer observed.

Remarkably, we noticed that there exists a distinct narrow range of oxygen content inside the superconducting regime [see the shaded area in Fig. 6(a)]. Within this regime, the oxygen content in La₃Ni₂O₇ closely approaches 7, and the corresponding normal-state resistance of the sample exhibits metallic behavior. By contrast, outside this regime, the normal-state resistance exhibits semiconducting-like behavior, and there is a prominent upturn at low temperature. These observations indicate the crucial role of the stoichiometric oxygen content in determining the presence of a metallic normal state and a superconducting state at low temperature in this material.

Modulated ac susceptibility measurements were also conducted on the same polycrystalline samples that we used for the resistance measurements. Not surprisingly, we did not observe any superconducting diamagnetic signal in the samples with oxygen content ranging from 6.88 to 7.42 [see Figs. 6(b)–6(e)]. Therefore, we propose that the superconducting volume fraction in these polycrystalline samples should be less than 0.5%, which is the limit of detection of our measuring system (see supplementary material).

On the basis of these observations, we make the following points addressing various perplexing issues:

1. Despite the dominant phase of the single-crystal sample being the 327 phase, the 327 phase itself should not be considered responsible for the superconductivity, because only ∼1% superconducting volume fraction has been observed in the material.

2. Owing to the lower T_c value (∼20 K) of the 4310-phase sample compared with that of the 327-phase sample, it is implausible that the observed superconducting transition near 80 K observed in La₃Ni₂O₇ arises from pure 4310 phase.

3. The fact that there is coexistence of the 327 and 4310 phases in both single-crystal and polycrystalline samples leads us to propose that the filamentary-like superconductivity is most likely located at the interface between these phases.

4. Although we detected a polymorph with a 1313 stacking sequence in one of the single-crystal samples using single-crystal XRD (see the supplementary material), our STEM investigations of both single-crystal and polycrystalline samples did not find this polyform to be present. The absence of the 1313 phase in the samples used in our STEM investigations suggests that the La₃Ni₂O₇ samples exhibit significant inhomogeneity. Further investigations are imperative to explore whether filamentary superconductivity is linked to the 1313 phase. It is important to highlight that the 4310 phase from the outer layer of the 1313 phases can also create an interface between the 327 and 4310 phases, which aligns with our proposal regarding the potential location of filamentary superconductivity, specifically at the interface between the 327 and 4310 phases.

In conclusion, we are the first to confirm the existence of high-temperature superconductivity in La₃Ni₂O₇ through demonstrating zero resistance and superconducting diamagnetism, and we subsequently propose that the nature of the observed superconductivity is filamentary-like. These findings provide vital insights into the anomalous superconducting behavior of compressed La₃Ni₂O₇. Furthermore, our measurements of resistance and ac susceptibility consistently demonstrate the reversibility of pressure-induced superconductivity, indicating that the superconducting phase exists in a metastable state. Our STEM investigations of both single-crystal and polycrystalline samples of La₃Ni₂O₇ have revealed that the observed filamentary-like superconductivity in this material most likely emerges at the interface between 327 and 4310 phases. If this is case, it is reasonable to anticipate that enhancing this interface is a potential route to increasing the superconducting volume fraction.⁶⁸ Further, we have determined the upper and lower bounds of the oxygen content for the presence of superconductivity in compressed La₃Ni₂O₇ as ∼7.35 and 6.89, respectively.

Our findings then raise significant questions that warrant further investigation:

• Why does the coexistence between the 327 and 4310 phases result in the development of high-T_c superconductivity?

• Is the valence change of Ni ions in compressed La₃Ni₂O₇ related to its superconductivity?

• Why is the stoichiometric oxygen content favorable for the presence of superconductivity?

Addressing these questions may not only provide deeper insights into the physics underlying the superconductivity in this nickelate, but also give effective guidance for exploring new high-T_c superconductors in 3d transition metal compounds.